MT (mobile terminated) is a message delivered to a phone; MO (mobile originated) is a message sent from a phone, for example a reply or a STOP.
Carriers name messages by where they end. A mobile-terminated message ends on a handset: everything a gateway sends on your behalf is MT. A mobile-originated message starts on a handset: a reply, a keyword, an opt-out. Pricing, routing and reporting are different for each direction, and MO traffic needs a number that can receive.
Delivery receipts describe MT messages; inbound webhooks describe MO messages. When a provider quotes an "SMS price" it is the MT price; MO is usually free to receive but implies renting a number.
At SMSMeteor: the rate card is MT pricing per destination; MO replies require a two-way number and arrive as inbound events.